Inference for Classes of Processes

Abstract

This chapter is devoted to specific problems of inference for both the continuous and discrete indexed processes. The hypothesis testing, estimation and certain (unbiased) weighted prediction problems together with some calculations of likelihood ratios for processes are detailed. In the discrete indexed cases, an analysis of the asymptotic properties of estimators for some classes is also given. Principles outlined in the preceding chapters on classical (finite sample) cases are utilized and improved upon for the types of processes considered. The sequential testing aspect is included with an extended treatment as it motivates solving several new and important questions using stopping times, both in probability and inference theories. Processes defined by difference equations and estimation problems for their parameters are also treated. These indicate the depth and a feeling for the general theory. This chapter contains an essential and important part of analysis studied in the present work. Various aspects of this study will be analyzed in greater detail for many specialized problems in the ensuing chapters, as they play key roles.